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Mirrors > Home > ILE Home > Th. List > iunss | Unicode version |
Description: Subset theorem for an indexed union. (Contributed by NM, 13-Sep-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
iunss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iun 3659 | . . 3 | |
2 | 1 | sseq1i 2969 | . 2 |
3 | abss 3009 | . 2 | |
4 | dfss2 2934 | . . . 4 | |
5 | 4 | ralbii 2330 | . . 3 |
6 | ralcom4 2576 | . . 3 | |
7 | r19.23v 2425 | . . . 4 | |
8 | 7 | albii 1359 | . . 3 |
9 | 5, 6, 8 | 3bitrri 196 | . 2 |
10 | 2, 3, 9 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wcel 1393 cab 2026 wral 2306 wrex 2307 wss 2917 ciun 3657 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-in 2924 df-ss 2931 df-iun 3659 |
This theorem is referenced by: iunss2 3702 djussxp 4481 fun11iun 5147 |
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